In a large scale environment like an open-cut mine, spatial modeling of geography and geology can have many uses in planning, analysis and operations within the environment. In the case of automated mining, a geographical model or terrain map can be used to guide robotic vehicles, whilst an in-ground geological model of the ore body may be used to determine drilling and blasting operations.
A digital representation of the operating environment in the form of a spatial model is typically generated from sensor measurements which provide a sample of the actual environmental variable being modeled (e.g. elevation in the case of a terrain map, or ore grade in the case of in-ground ore body modeling) at various spatially distinct locations within the operating environment. The measured sample data is then treated in some manner such as by interpolation to determine information about the environment in locations other than those actually measured.
State-of-the-art representations generally map surfaces by computing triangulations. These methods, however, do not have a statistically sound way of incorporating and managing uncertainty. The assumption of statistically independent data is a further limitation of many works that have used these approaches. While there are several interpolation techniques known, the independence assumption can lead to simplistic (simple averaging like) techniques that result in an inaccurate modeling of the terrain.
Gaussian process based terrain modeling provides an approach that enables a multi-resolution representation of space, incorporates and manages uncertainty in a statistically sound way, and can handle spatially correlated data in an appropriate manner. Gaussian Processes (GPs) are stochastic processes based on the normal (Gaussian) distribution and can be used to good effect as a powerful nonparametric learning technique for spatial modeling. Inference of continuous values with a Gaussian process prior is known as Gaussian process regression, and is sometimes referred to as “Kriging” in the geospatial community.
Another difficulty in terrain modeling arises from the limited perceptual capabilities and/or placement opportunities for measurement sensors which renders collected sensory data notably incomplete. Incomplete sensor data can be manifested in a number of different ways. Sensors have an inherent field-of-view and range which limit the region of terrain that can be measured at one time. If the region of interest is larger then multiple sensors (or multiple measurements with one sensor) would be needed to obtain sample measurements across the whole area. Physical occlusions within a sensor field-of-view may also cause incomplete measurement data requiring another sensor placement. Further, various different kinds of sensors may be used to measure terrain in the same region. For example, terrain data can be obtained using numerous sensors including 3D laser scanners and GPS. Laser scanners (sometimes referred to as LIDAR sensors) provide dense and accurate data, whereas a GPS based survey typically comprises a relatively sparse set of well chosen points of interest.
In large scale terrain modeling it may therefore be useful to incorporate multiple sensory snapshots from multiple sensors to obtain the most complete model possible. This will require fusing these multiple and multi-modal sensory datasets to obtain a unified computational model.